These can be the focus of 2 to 3 questions at the exam, therefore know the differences:
System status checks monitor the AWS systems on which your instance runs
Problem with the underlying host. Example:
Loss of network connectivity
Loss of system power
Software issues on the physical host
Hardware issues on the physical host that impact network reachability
Either wait for AWS to fix the host, OR
Move the EC2 instance to a new host = STOP & START the instance (if EBS backed)
Instance status checks monitor the software and network configuration of your individual instance
Example of issues
Incorrect networking or startup configuration
Exhausted memory
Corrupted file system
Incompatible kernel
Requires your involvement to fix
Restart the EC2 instance, OR
Change the EC2 instance configuration